harvard-smithsonian center for astrophysics patrick slane surface emission from neutron stars

Harvard-Smithsonian Center for AstrophysicsPatrick Slane

Surface Emission

from Neutron Stars


- COMPOSITION? -- pions, kaons, quarks?

- COMPOSITION? -- H, He, Fe?

- HOW STRONG? -- affects opacity -- cyclotron features?

- SUPERFLUID CONTRIBUTIONS? -- strongly affect emissivity

-PULSAR WIND? -- that nasty nonthermal emission


Neutron Star Cooling: An Introduction

• NS Structure is modeled like any star: - hydrostatic equilibrium - energy balance between production & radiation - energy transport

• Auxiliary equations relating these are: - equation of state, describing pressure conditions - opacity equation, regulating energy transport - emission equation, yielding energy input

Why is this Complicated?

• Superfluid state is not well constrained - critical temperature and energy gap for proton and neutron superfluid states not well known - strongly affects emissivity, as thermal properties change dramatically under superfluid conditions variety of superfluid models exist∴

• Composition is not well known - details of strong interactions at ultrahigh densities are uncertain variety of EOS models exist∴

∴

• emissivity depends critically on presence/absence of pions/kaons/etc - “standard” emissivity is from modified URCA process and bremsstrahlung - pion-induced -decay proceeds at a much higher rate; presence or absence of pions is thus crucial to cooling rate (and same is true of kaons and quarks) “standard” and “exotic” cooling models exist


How Does the Neutron Star Interior Cool?

• NS matter is highly degenerate

FEkTT MeV 0.01 K;10 9 <<<<

~kT

n p e

Fer

mi E

nerg

y (M

eV)

20

40

60

100

200

300

Ferm

i Mom

entum (M

eV/c)

• Momentum conservation requires

• Charge neutrality requires:

€

EF =h2

8m

3n

π

⎛

⎝ ⎜

⎞

⎠ ⎟2 / 3

€

ρb ≈ 2.8 ×1014 g cm−3

?05.0/Yp ≈= bp nn

FF mEp 2=

Urca process:eepn ++→ −

enep υ+→+ −

)()( ppepnn FFpe =⇒=

nep ppp ≥+

particles allfor ~ kTEE F−∴

0)(2)(2)(2 ≥−+= nEmeEmpEm FnFeFpχ

• We thus require

- momentum can only be conserved for Urca reactions if proton fraction is >0.12 - for lower values, need bystander particle to conserve momentum


Cooling Curves: Standard vs. Exotic Cooling• Urca reactions:

eepn ++→ −

enep υ+→+ −(-decay)

(inv. -decay)- cannot conserve energy and momentum in highly degenerate NS core

• Pion cooling- if pion condensates exist in core, rate is enhanced

eenn π ++→+ −−

enen υπ ++→+ −−

69

246104.1 TM

ML nuc

⎟⎟⎠

⎞⎜⎜⎝

⎛×=

Θ ρρθπ

• Kaon condensates or free quarks also enhance rate - degree to which exotic particles exist in core depends on EOS - EOS is not well known because many-body modeling of strong interactions at ultrahigh densities isn’t well understood

• Superfluidity strongly affects rate - rapid cooling is delayed - details poorly understood/ heavily model dependent

• In some equations of state, proton fraction in core is high enough for direct Urca cooling - cooling rate is increased even above pions, etc. - unclear if this occurs before presence of exotic particles

“Standard” cooling dominatedby Modified Urca in core

eepnnn +++→+ −

ennepn υ++→++ −

- lower reaction rate

89

3/1

39103.5 TM

ML nucMUrca

⎟⎟⎠

⎞⎜⎜⎝

⎛×=

Θ ρρ

- MUrca adds bystander:

Page 1998


NS Cooling (cont.)

Ho & Lai 2001

Yakovlev & Pethick 2004

• For sufficiently high densities, direct Urca cooling proceeds - for a given equation of state, this corresponds to the possibility of dUrca onset for more massive stars

• Superfluidity moderates rapid cooling - different models for energy gap yield different cooling paths

• X-ray observations of young neutron stars provide constraints on cooling models - current observations can all be explained within context of above cooling scenarios - dUrca (or other) rapid cooling appears required for several young NSs, possibly indicating a distribution in NS masses


NS Atmospheres• The emission from a NS surface is significantly modified by the presence of an atmosphere - atmosphere is highly compressed; scale height is ~0.1-10 cm, density is of order 0.1-1000 gm/cc; not an ideal gas!

• Any small amount of accretion from fallback or ISM is sufficient to form an optically thick atmosphere - composition and stratification depends on equation of state; upper layer most likely H, but burning could yield He - without accretion, expect mostly Fe

• Opacity is a function of temperature, density, and composition - emission from different optical depths sample different temperatures - result is a spectrum that deviates from a blackbody, with emission extending beyond Wien tail - line features result, particularly for heavy element atmospheres (e.g. Fe)

Temperature vs opacity depth for scattering (upper) and absorption (lower)

Ho & Lai 2001


NS Atmospheres• The emission from a NS surface is significantly modified by the presence of an atmosphere - atmosphere is highly compressed; scale height is ~0.1-10 cm, density is of order 0.1-1000 gm/cc; not an ideal gas!

• Any small amount of accretion from fallback or ISM is sufficient to form an optically thick atmosphere - composition and stratification depends on equation of state; upper layer most likely H, but burning could yield He - without accretion, expect mostly Fe

• Opacity is a function of temperature, density, and composition - emission from different optical depths sample different temperatures - result is a spectrum that deviates from a blackbody, with emission extending beyond Wien tail - line features result, particularly for heavy element atmospheres (e.g. Fe)

Ho & Lai 2001

Zavlin et al. 1996


NS Atmospheres (cont.)

• When B > 10 G, properties of atoms are completely different from B = 0 case - cyclotron radius is

- for large B, this is smaller than Bohr radius of atom - Coulomb force is more effective in binding electrons along B field, and atoms attain a cylindrical structure - for B = 10 G, ionization potential for H atom is 160 eV (compare with 13.6 eV for B = 0)

• Motion is quantized to Landau levels with

- cyclotron absorption features result - can get multiple harmonics - opacity increases near (not just at) broader lines - range of B-field strength on surface also contributes to broadening

9

12

c



Optical depth, temperature, and density at point from which photons of a given energy originate (Ho & Lai2001).

• Polarization effects in magnetized plasma modify the resultant spectrum. Two modes: - ordinary (O) mode: photon electric field vector in k-B plane - extraordinary (X) mode: photon electric field vector perpendicular to k-B plane

• Opacity is higher for O-mode (since electrons/ions can absorb easily along B) - X-mode samples higher temperatures and dominates spectrum (thus emission is polarized) - cyclotron absorption is significant for X-mode (and thus overall)

• He atmospheres very similar to H, except for position of cyclotron resonances

• Ionization balance difficult to calculate - full ionization typically assumed, though recent work done on partial ionization

electricvector

k



Hydrogen model for magnetic atmosphere. (Ho & Lai 2001).

• Polarization effects in magnetized plasma modify the resultant spectrum. Two modes: - ordinary (O) mode: photon electric field vector in k-B plane - extraordinary (X) mode: photon electric field vector perpendicular to k-B plane

• Opacity is higher for O-mode (since electrons/ions can absorb easily along B) - X-mode samples higher temperatures and dominates spectrum (thus emission is polarized) - cyclotron absorption is significant for X-mode (and thus overall)

• He atmospheres very similar to H, except for position of cyclotron resonances

• Ionization balance difficult to calculate - full ionization typically assumed, though recent work done on partial ionization

electricvector

k


NS Atmospheres (cont.)• Vacuum polarization effects modify atmosphere spectrum for very large fields - polarization of atmosphere due to virtual e e pairs becomes significant above quantum critical field

- dielectric properties of medium are modified; scattering and absorption opacities are affected - where effects of plasma and vacuum on the linear polarization cancel, a resonance occurs:

- results in broad depression because of large density range in atmosphere

• Mode conversion can occur as photon traverses resonant density - converts one polarization mode to another (analogous to MSW effect for neutrino oscillations) - since the two modes have very different opacities, this conversion strongly affects spectrum

+ -

from W. Ho


NS Atmospheres (cont.)• Vacuum polarization effects modify atmosphere spectrum for very large fields - polarization of atmosphere due to virtual e e pairs becomes significant above quantum critical field

- dielectric properties of medium are modified; scattering and absorption opacities are affected - where effects of plasma and vacuum on the linear polarization cancel, a resonance occurs:

- results in broad depression because of large density range in atmosphere

• Mode conversion can occur as photon traverses resonant density - converts one polarization mode to another (analogous to MSW effect for neutrino oscillations) - since the two modes have very different opacities, this conversion strongly affects spectrum

+ -

Ho & Lai 2003


Neutron Star Emission: Gravitational Effects• Layering of atmosphere - EOS determines density/temperature distribution (as discussed above)

• Gravitational redshift:

- affects inferred temperature and luminosity - for discrete lines, redshift gives M/R (line detection thus important!) - total flux gives R (for known distance and measured temperature)

- thus, can get M (assuming R represents total surface)

• Pulsed fraction - pulsed thermal emission results from compact emission regions on surface - smaller region produces larger PF - however, gravitational bending of light smears out the contrast - can get very small PF even for very small emitting regions

€

Ts∞ = Ts 1−

2GM

c 2R

€

Lγ∞ = Lγ 1−

2GM

c 2R

⎡ ⎣ ⎢

⎤ ⎦ ⎥

€

R∞2 =

Lγ∞

4πσ (Ts∞)4

€

R∞ = R 1−2GM

c 2R

⎡ ⎣ ⎢

⎤ ⎦ ⎥

−1/ 2€

λλ0

= 1−2GM

c 2R

Psaltis et al. 2000

0.1

1.0 R/M = 12 km/Msun R/M = 9 km/Msun R/M = 6 km/Msun


• GR effects dramatically affect observable modulation - large emitting regions or M/R ratios yield low pulsed fractions

• Size of emitting region limits the blackbody-like flux - tradeoff off between pulsed fraction and observed flux

• For AXPs, some appear to have emitting areas too large to explain observed pulsed fractions - indicative of incorrect atmosphere yielding luminosity that is too high?

∴xL

Pulse Profile and Emission Geometry

One hot spot

Ozel 2002


RX J1856.5-3754 is a nearby isolated neutron star first identified inobservations with the ROSAT observatory. It is sufficiently nearby thatHST observations yield a parallax distance, d = 120 pc. Its X-rayspectrum is well-fit by a blackbody model with a temperature of The associated bolometric flux is .

What is the observed radius of the emitting region? Compare this withpredictions of NS radii from equation-of-state calculations (Figure 1).What can be concluded about the nature of RX J1856.5-3754?

If the observed blackbody emission is the result of a small emission regionon the NS surface, one might expect pulsations as the star rotates.Gravitational light bending reduces the expected pulsed fraction. Unfavorableviewing geometry can also reduce or eliminate pulsations (Figure 2).

Timing measurements for RX J1856.5-3754 yield no evidence for pulsations,with an upper limit of 5% on the pulsed fraction. Can the pulsed fractionlimit be reconciled with the observed blackbody spectrum while still beingconsistent with the sources being a neutron star?

Psaltis et al. 2000

0.1

1.0 R/M = 12 km/Msun R/M = 9 km/Msun R/M = 6 km/Msun

Mass-Radius Constraints From NS EOS Models

See Ransom et al. 2002, 570, L75; Walter 2004, J. Phys. G: Nucl. Part. Phys. 30 S461


RX J185635-3754: An Old Isolated NS(?)

• Distance known well from parallax - d = 117 +- 12 pc (Walter & Lattimer 2002)

• X-ray emission consistent with blackbody - no lines seen despite 450 ks Chandra LETG observation; rules out heavy element atmosphere - kT = 63 eV; R = 4.3 km at d = 117 pc - this is too small for a neutron star! (quark star??!!)

• X-ray BB spectrum under-predicts optical/UV flux - model with two BBs needed; 27 eV and 64 eV - then - but smaller size still needed for X-rays; hot spot - no quark star needed…

• No pulsations observed - pulsed fraction < 5%; how can this be? - GR bending (hard to reconcile with optical radius)

€

R∞ =17 ±1.9 km

• Recent atmosphere model holds promise (Ho et al. 2006) - emission from partially-ionized H yields reasonable NS size and log B ~ 12.6 - but, need very thin atmosphere so that not optically thick at all temp; how does this arise???

harvard-smithsonian center for astrophysics patrick slane surface emission from neutron stars

Documents